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arXiv · 2502.17950

The regularity of electronic wave functions in Barron spaces

Harry Yserentant
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Abstract

The electronic Schr\"odinger equation describes the motion of $N$ electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenvalues below the essential spectrum lie in the spectral Barron spaces $\mathcal{B}^s(\mathbb{R}^{3N})$ for $s<1$. The example of the hydrogen ground state shows that this result cannot be improved.

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Harry Yserentant. 2025-02-25. The regularity of electronic wave functions in Barron spaces. https://doi.org/10.1051/m2an%2F2026015

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